2 problems

Constant-depth Frege oddtown conjecture. For each $d\in\mathbb{N}$ and each prime $p\neq 2$,

Let $\mathsf{KS}$ be the minimal complete fragment of a standard deep inference system for propositional logic, and let $\mathsf{KS}\cup\{\mathsf{c\!\uparrow}\}$ denote its extensi…